Can I add a required field, such as a tick box for the confirmation of reading the Terms and Conditions, or for the provision of next of kin details, etc?
Within a Form, there isn't the option of a required field on other Form Elements other than the Communication Preferences and Contact details, however...
You can add an Activity Element with a custom field of 'Read T&Cs?' or 'Next of Kin Name', etc and then use that field in asking a question on your Form.
You can make a note in your text that it is a required field so that the person completing the Form is aware it is needed.
To report on the completion of the required element, create a List that is filtered by the Activity and where that particular custom field is empty.
You can then follow this up manually with the Constituent, e.g by phone or by email, or you can use a more automated approach and use a Trigger. Your Trigger can be set to automatically send an email to the constituent asking them to confirm via email. (see Triggers)
When that email is received, you can then attach their confirmation to the Activity and edit the Activity manually so that it is shown as confirmed.